I have a similar issue with my neighbour. The problem is they live abroad and let the property out and are pretty much un-contactable. The tree is getting very big now and needs reducing in height before it starts causing issues (in fact it constantly blocks the gutters which their letting agent pays to get cleared and charges them for). They do not seem to care at all though. I had a few problem trees (conifers) removed recently and managed to get them a vastly reduced quote for a professional prune. They did not take it up preferring their own (or the letting agents own) contractor, who was not a professional tree surgeon and who quoted a huge amount more...so in the end, they did not get it done! I am thinking of offering to pay to get it done if they are going to be that stingy....as it will end up damaging both our properties.
Anyway...back to topic....
...Unfortunately, as far as I am aware, you have no authority or legal right to do anything. You can only trim any overhanging branches that go to your side of the boundary. I think you "legally" have to offer these back to your neighbour or something.....
Howvever, in your specific case it may be an idea to contact the power distribution board for your area. They may have the power to require your neighbour to cut back the tree on safety grounds...
First though.....have you actually talked to them?